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1

Let's take the example of the unsteady one-dimensional heat equation inside a solid on a domain $x\in[0,1]$: $$\partial_t u - D\partial_{xx} u = 0$$ with the initial profil $u(0,x) = u_0(x)$ at $t=0$, and Dirchlet boundary conditions enforcing that the wall at $x=0$ (respectively $x=1$) is at temperature $u_{L}$ (respectively $u_{R}$). If we use discretise ...


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Have you plotted the solution using a visualization package or just a cut through the middle of your domain? Sometimes just looking at the solution you're generating will give you an insight into where it's arising from. Based on your description, I'd say there's a mistake in your implementation of your boundary condition. ETA: The last sentence is probably ...


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This maybe raises more questions than it answers, but here is what I think one should do. Lets assume that at the boundary point p, the velocity u is defined as $$ u(p) = u_1 \phi_k(p) + u_2 \phi_{k+1} (p), $$ where $$\phi_k = \begin{bmatrix} \phi \\ 0 \end{bmatrix}, \quad \phi_{k+1} = \begin{bmatrix} 0 \\ \phi \end{bmatrix} $$ are corresponding nodal basis ...


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